Asymptotically-Stable Adaptive-Optimal Control Algorithm with Saturating Actuators and Relaxed Persistence of Excitation

This paper proposes a control algorithm based on adaptive dynamic programming to solve the infinite-horizon optimal control problem for known deterministic nonlinear systems with saturating actuators and non-quadratic cost functionals. The algorithm is based on an actor/critic framework where a critic neural network is used to learn the optimal cost and an actor neural network is used to learn the optimal control policy. The adaptive control nature of the algorithm requires a persistence of excitation condition to be a priori validated, but this can be relaxed by using previously stored data concurrently with current data in the update of the critic neural network. A robustifying control term is added to the controller to eliminate the effect of residual errors, leading to asymptotically stability of the closed-loop system. Simulation results show the effectiveness of the proposed approach for a controlled Van-der Pol oscillator and also for a power systems plant.